Abstract
In this paper we discuss locking and robustness of the finite element method for a model circular arch problem. It is shown that in the primal variable (i.e., the standard displacement formulation), the p-version is free from locking and uniformly robust with order\(p^{-k}\) and hence exhibits optimal rate of convergence. On the other hand, the h-version shows locking of order \(h^{-2}\), and is uniformly robust with order \(h^{p-2}\) for \(p>2\) which explains the fact that the quadratic element for some circular arch problems suffers from locking for thin arches in computational experience. If mixed method is used, both the h-version and the p-version are free from locking. Furthermore, the mixed method even converges uniformly with an optimal rate for the stress.
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